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Explain solution RD Sharma class 12 chapter Functions exercise 2.1 question 22 maths

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Let f:R\rightarrow R given by f_1(x)=x-[x]

To prove:

The given function is neither one-one nor onto.


First we will check whether the given function is one-one or not.

For one-one; we have,

\therefore f(x)=x-[x]

\Rightarrow f(x)=0 for all x\in R

\therefore f is not one-one where as many-one.

Again, Range (f)=[0,1) \neq R

\therefore f is not onto.

Hence f is neither one-one nor onto.

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